Homological algebra for the representation Green functor for abelian groups

Author:
Joana Ventura

Journal:
Trans. Amer. Math. Soc. **357** (2005), 2253-2289

MSC (2000):
Primary 55P91, 18G10

DOI:
https://doi.org/10.1090/S0002-9947-04-03566-4

Published electronically:
May 10, 2004

MathSciNet review:
2140440

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we compute some derived functors of the internal homomorphism functor in the category of modules over the representation Green functor. This internal homomorphism functor is the left adjoint of the box product.

When the group is a cyclic -group, we construct a projective resolution of the module fixed point functor, and that allows a direct computation of the graded Green functor .

When the group is , we can still build a projective resolution, but we do not have explicit formulas for the differentials. The resolution is built from long exact sequences of projective modules over the representation functor for the subgroups of by using exact functors between these categories of modules. This induces a filtration which gives a spectral sequence which converges to the desired functors.

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Additional Information

**Joana Ventura**

Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

Email:
jventura@math.ist.utl.pt

DOI:
https://doi.org/10.1090/S0002-9947-04-03566-4

Received by editor(s):
August 22, 2003

Published electronically:
May 10, 2004

Additional Notes:
The author was partially supported by FCT grant Praxis XXI/BD/11357/97 and a one year research grant from Calouste Gulbenkian Foundation

Article copyright:
© Copyright 2004
American Mathematical Society